"I'm seriously thinking about maybe giving another opportunity for you to vote for or against me in a few years from now," McCain said on KFYI-AM in Phoenix, according to The Washington Post. "I'm seriously giving that a lot of thought."

McCain had previously suggested he's considering retiring rather than run for a sixth term in 2016, when he'll be 80.

In September, McCain joked that “the president and I, he's in his last term; I'm probably in mine. The relationship we have had over the past three years is quite good."

He then said he hadn't yet made a decision, but that he doesn't "want to be one of these old guys that should've shoved off."

McCain said on Tuesday that he's getting encouragement from business leaders, who he said were incensed by the shutdown, to run.

"I'm certainly getting a lot of encouragement from our business community, who's overwhelmingly upset about what we did, shutting down the government, because of what it did to their businesses and Arizona's economy," he said.

McCain has easily won reelection each term, never receiving less than 56 percent of the vote. Though he's likely to face a Tea Party challenger in 2016 if he runs again, he easily defeated a primary opponent in 2010, during the height of the Tea Party movement.